Maria is a free-spirited young Austrian woman studying to become a nun at Nonnberg Abbey in Salzburg in 1938. Her youthful enthusiasm and lack of discipline cause some concern. Mother Abbess sends Maria to the villa of retired naval officer Captain Georg von Trapp to be governess to his seven children—Liesl, Friedrich, Louisa, Kurt, Brigitta, Marta and Gretl. The Captain has been raising his children using strict military discipline following the death of his wife. They have scared away several governesses by playing tricks. Although the children misbehave at first, Maria responds with kindness and patience, and soon the children come to trust and respect her.

While the Captain is away in Vienna, Maria makes play clothes for the children out of drapes that are to be changed. She takes them around Salzburg and the mountains while teaching them how to sing. When the Captain returns to the villa with Baroness Elsa Schraeder, a wealthy socialite, and their mutual friend Max Detweiler, they are greeted by Maria and the children returning from a boat ride on the lake which concludes when their boat overturns. Displeased by his children's clothes and activities and Maria's impassioned appeal that he get closer to his children, the Captain attempts to fire Maria. However, he hears singing coming from inside the house and is astonished to see his children singing for the Baroness. Filled with emotion, the Captain joins his children, singing for the first time in years. The Captain apologizes to Maria and asks her to stay.

Impressed by the children's singing, Max proposes that he enters them in the upcoming Salzburg Festival, but the Captain disapproves of letting his children sing in public. During a grand party at the villa, where guests in formal attire waltz in the ballroom, Maria and the children look on from the garden terrace. When the Captain notices Maria teaching Kurt the traditional Ländler folk dance, he steps in and partners Maria in a graceful performance, culminating in a close embrace. Confused about her feelings, Maria blushes and breaks away. Later, the Baroness, who noticed the Captain's attraction to Maria, hides her jealousy by indirectly convincing Maria that she must return to the abbey.

However, Mother Abbess learns that Maria has stayed in seclusion to avoid her feelings for the Captain, so she encourages her to return to the villa to look for her purpose in life. When Maria returns to the villa, she learns about the Captain's engagement to the Baroness and agrees to stay until they find a replacement governess. However, the Baroness learns that the Captain's feelings for Maria haven't changed, so she peacefully calls off the engagement and returns to Vienna while encouraging the Captain to express his feelings for Maria, who marries him.

While the couple is on their honeymoon, Max enters the children into the Salzburg Festival against their father's wishes. Having learned that Austria has been annexed by the Third Reich, the couple return to their home, where the Captain receives a telegram, ordering him to report to the German Naval base at Bremerhaven to accept a commission in the Kriegsmarine. Strongly opposed to the Nazis and their ideology, the Captain tells his family they must leave Austria immediately.

That night, the von Trapp family attempt to flee to Switzerland, but they are stopped by a group of Brownshirts, led by the Gauleiter Hans Zeller, waiting outside the villa. To cover his family's tracks, the Captain maintains they are headed to the Salzburg Festival to perform. Zeller insists on escorting them to the festival, after which his men will accompany the Captain to Bremerhaven.

Later that night at the festival, during their final number, the von Trapp family slips away and seeks shelter at the abbey, where Mother Abbess hides them in the cemetery crypt. Zeller and his men soon arrive and search the abbey, but the family is able to escape using the caretaker's car. When they attempt to pursue, they discover their cars will not start, as two of the nuns have sabotaged their engines. The next morning, after driving to the Swiss border, the von Trapp family make their way on foot across the frontier into Switzerland to safety and freedom.